81-4b^2-16=0

Solution for 81-4b^2-16=0 equation:

81-4b^2-16=0

We add all the numbers together, and all the variables

-4b^2+65=0

a = -4; b = 0; c = +65;
Δ = b2-4ac
Δ = 02-4·(-4)·65
Δ = 1040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{65}}{2*-4}=\frac{0-4\sqrt{65}}{-8}
=-\frac{4\sqrt{65}}{-8}
=-\frac{\sqrt{65}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{65}}{2*-4}=\frac{0+4\sqrt{65}}{-8}
=\frac{4\sqrt{65}}{-8}
=\frac{\sqrt{65}}{-2}
$